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On the Shape Transformation of Cone Scales
Abstract
The shape-morphing behaviours of some biological systems have drawn considerable interest over many years. This paper divulges that the opening and closing mechanism of pine cones is attributed to the self-bending of their scales, which undergo three states of humidity-driven deformation in terms of Föppl-von Kármán plate theory. Both numerical simulation and experimental measurement support the theoretical analysis, showing that the longitudinal principal curvature and the transverse principal curvature bifurcate at a critical humidity level according to the thickness and shape of scales. These findings help us understand the shape transformation of bilayer or multi-layer natural structures and gain insights into the design of transformable devices/materials with great potential in numerous applications.
... We propose the following pine cone initial opening actuation scenario: A mature, closed cone possesses tight resin seals between its individual, wet and bent scales. Under dry conditions in spring, the scales evaporate water and "try" to bend outwards (which would lead to the opening the cone), which is hindered by the resin seals as well as overlaying scales in the Fibonacci series (Lin et al., 2016). Upon suitable conditions regarding temperature and humidity, the forces generated by the hydraulically actuated scales in combination with the temperature-induced alterations of the resin's rheological properties lead to stochastic seal rupture events. ...
... The random scale movements during initial opening are contradictory to previous publications that assumed an opening according to the Fibonacci-series in which scales are arranged (Kilmer, 1971;Lin et al., 2016), which in our experiments occurred only from the second opening events onwards. We also observed simultaneous strain developments in between all apophyses in subsequent opening events, which is most probably due to breakage of the resin seals between the scales. ...
... During wetting, the scale dry weights increased on average by about 61.5%, which leads to the typical bending into the closed state of the respective cone (Lin et al., 2016). Some scales nearly doubled their weight (90% increase) during water uptake. ...
Pine cones show functionally highly resilient, hygroscopically actuated opening and closing movements, which are repeatable and function even in millions of years old, coalified cones. Although the functional morphology and biomechanics behind the individual seed scale motions are well understood, the initial opening of the cone, which is often accompanied by an audible cracking noise, is not. We therefore investigated the initial opening events of mature fresh cones of Scots pine (Pinus sylvestris) and their subsequent motion patterns. Using high-speed and time lapse videography, 3D digital image correlation techniques, force measurements, thermographic and chemical-rheological resin analyses, we are able to draw a holistic picture of the initial opening process involving the rupture of resin seals and very fast seed scale motion in the millisecond regime. The rapid cone opening was not accompanied by immediate seed release in our experiments and, therefore, cannot be assigned to ballistochory. As the involved passive hydraulic-elastic processes in cracking are very fine-tuned, we hypothesize that they are under tight mechanical-structural control to ensure an ecologically optimized seed release upon environmental conditions suitable for wind dispersal. In this context, we propose an interplay of humidity and temperature to be the external “drivers” for the initial cone opening, in which resin works as a crucial chemical-mechanical latch system.
... The length of the fiber components remains constant, and the porous components shirks when dry and swells when hydrated, which causes the local strain to increase monotonically as the distance from the fiber layer increases. The two-layer scale structure of pine cone can be regarded as a 3D structure that provides an idea for the construction of the bionic model of a pine cone ( Figure 3D) (Reyssat and Mahadevan, 2009;Lin et al., 2016;Dawson et al., 1997;Hellum, 1982). Lin et al. revealed that the pine cone's opening and closing mechanism was due to the self-bending action of its scales. ...
... They found that at critical humidity levels the longitudinal and transverse principal curvature bifurcated according to the thickness and shape of the scale. These findings help to understand the shape transformation of double or multilayer natural structures and provide insights into the design of convertibles/materials with great application potential (Lin et al., 2016). ...
... (D) The geometry model of pine cone and the deformation diagram. The state of pine cone under wet and dry conditions and their SEM images(Reyssat and Mahadevan, 2009;Lin et al., 2016). ...
Nature does nothing in vain. Through millions of years of revolution, living organisms have evolved hierarchical and anisotropic structures to maximize their survival in complex and dynamic environments. Many of these structures are intrinsically heterogeneous and often with functional gradient distributions. Understanding the convergent and divergent gradient designs in the natural material systems may lead to a new paradigm shift in the development of next-generation high-performance bio-/nano-materials and devices that are critically needed in energy, environmental remediation, and biomedical fields. Herein, we review the basic design principles and highlight some of the prominent examples of gradient biological materials/structures discovered over the past few decades. Interestingly, despite the anisotropic features in one direction (i.e., in terms of gradient compositions and properties), these natural structures retain certain levels of symmetry, including point symmetry, axial symmetry, mirror symmetry, and 3D symmetry. We further demonstrate the state-of-the-art fabrication techniques and procedures in making the biomimetic counterparts. Some prototypes showcase optimized properties surpassing those seen in the biological model systems. Finally, we summarize the latest applications of these synthetic functional gradient materials and structures in robotics, biomedical, energy, and environmental fields, along with their future perspectives. This review may stimulate scientists, engineers, and inventors to explore this emerging and disruptive research methodology and endeavors.
... Furthermore, the 3D multiphase deformation of scales [11], the influence of delamination on scale movement in cyclically actuated pine cones [12], and the optimal timing of initial cone opening [13][14][15][16][17][18] have been investigated ( Figure 1). Whereas the previous literature has described the arrangement of scales on the cone axis as a Fibonacci sequence, their interrelated movement sequences resulting from changes in environmental humidity [18][19][20] and the forces that they can produce have been little studied [9,18,21]. The relationship between the size of a motile plant structure, the time scale of the water displacement inside this structure, and the duration of movement was described by [22]. ...
Hygroscopic seed-scale movement is responsible for the weather-adaptive opening and closing of pine cones and for facilitating seed dispersal under favorable environmental conditions. Although this phenomenon has long been investigated, many involved processes are still not fully understood. To gain a deeper mechanical and structural understanding of the cone and its functional units, namely the individual seed scales, we have investigated their desiccation- and wetting-induced movement processes in a series of analyses and manipulative experiments. We found, for example, that the abaxial scale surface is responsible for the evaporation of water from the closed cone and subsequent cone opening. Furthermore, we tested the capability of dry and deformed scales to restore their original shape and biomechanical properties by wetting. These results shed new light on the orchestration of scale movement in cones and the involved forces and provide information about the functional robustness and resilience of cones, leading to a better understanding of the mechanisms behind hygroscopic pine cone opening, the respective ecological framework, and, possibly, to the development of smart biomimetic actuators.
... A failure to sufficiently reduce the moisture content of cones during the extraction process prevents seed movement within the scales 18 . For a long time now researchers have been studying phenomena involving wood that can adopt a deformed shape at a certain moisture content and then return to its original shape after absorbing water 51-53 as well as scale movements in conifer cones caused by their cellular structure [54][55][56][57][58][59] . Findings from such research can form the basis for analyzing multi-phase movement by artificial intelligence 60,61 . ...
The objective of this study was to determine the number of stages of cone drying and immersion that yield the maximum number of high quality seeds. Nine variants of the process were conducted; they differed in terms of dwell time in the drying chamber and water immersion time. Each extraction variant consisted of five drying steps (lasting 10, 8 or 6 h) and four immersion steps (5, 10 or 15 min). Each drying step was followed by cone shaking in a purpose-made laboratory drum. The process variants were evaluated and compared in terms of cone moisture content as well as the dynamics of seed yield and the quality of seeds obtained in the various steps. The seed yield coefficient, α, and the cone mass yield coefficient, β, were calculated. The studied process of seed extraction can be described using the Lewis empirical model for the second stage of drying with the b coefficient ranging from 0.34 to 0.60. Relatively higher initial and final moisture content was found for cones immersed for 15 min (more than 0.45 kgwater·kgd.w.⁻¹), while the lowest moisture content was found for those immersed for 5 min (less than 0.4 kgwater·kgd.w.⁻¹). The highest seed yield at the first and second steps was obtained in the 8 h_10 min variant (53% and 32%, respectively). In all five-step variants, the mean cone yield amounted to 65% of total seeds in the cones; seeds obtained from all variants were classified in quality class I. The procedure recommended for commercial seed extraction facilities consists of three 8 h drying steps and two 10 min immersion steps, with cone shaking in a drum to maximize seed yield. A shorter cone extraction process maintaining an acceptable level of seed extraction may reduce energy consumption by nearly 50%.
... Extrusion-based additive manufacturing, such as continuous filament fabrication [1] and 3D concrete printing [2], deposits materials layer-by-layer on a building platform to additively fabricate products. Because of the superior flexibility to produce complex geometrical shapes, these technologies have been widely applied in prototype fabrication [3], construction buildings [4], bionic structures [5], etc. The technology is a multiobjective optimization process with respect to the materials [6], printing precision [7], support optimization [8,9], stress state [10,11], etc. ...
In extrusion-based additive manufacturing, path filling patterns may significantly affect the printing process. To overcome printing defects incurred by path discontinuity, a Globally Continuous Hybrid Path (GCHP) is developed to solidly fill or partially fill connected domains. Discontinuous contour paths and single zigzag paths are constructed to generate locally continuous paths. These paths are subsequently connected by contour paths to render global continuity. To reduce underfilled areas without breaking path continuity, the boundaries of gap areas are evenly clipped and merged with the path. Sharp turns are optimized by fillet edges to alleviate the reduction in printing velocity. The construction results of variable shapes indicate that GCHP can continuously fill domains. The printing quality and mechanical performance of the proposed path are better than those of the previous scheme based on contour parallel paths. This study paves a new way to fabricate models using hybrid paths for extrusion-based additive manufacturing.
... Numerical topology optimization methods are broadly utilized to optimize the shapes of structures, considering specific target functions such as: minimization of the self-weight or maximization of the bearing capacity of a structure [1,2]. As a specific type of topology optimization algorithms, layout optimization methods optimize combinations of truss/beam members. ...
Discontinuity layout optimization (DLO) is a relatively new upper bound limit analysis method. Compared to classic topology optimization methods, aimed at obtaining the optimum design of a structure by considering its self-weight, building cost or bearing capacity, DLO optimizes the failure pattern of the structure under specific loading conditions and constraints by minimizing the dissipation energy. In this work, we present a modified DLO algorithm that contains all of the advantages of DLO. It is referred to virtual displacement-based discontinuity layout optimization (VDLO). VDLO takes the stress state of a loaded structure as a snapshot and correspondingly provides the optimum failure pattern, which greatly extends the application potential of DLO. Numerical examples indicate the effectiveness and flexibility of VDLO. It is regarded as a highly promising supplemental tool for other numerical methods in element-/node-based frameworks.
... As reported by Lin et al. [41] for Pinus pinaster cones, the cone opening and closing mechanism can be attributed to the self-bending of their scales, which undergo three states of humidity-driven deformation in terms of Föppl-von Kármán plate theory [42]. Based on three other reports [29,33,35], it may be concluded that it is moisture and the shape and size of cells that trigger opening and closing of cones. ...
The objective of the study was to elucidate the kinematics of cone opening in the European larch (Larix decidua Mill.) during a four-step seed extraction process and to determine optimum process time on that basis. Each step lasted 8 h with 10 min of water immersion between the steps. The study also described the microscopic cellular structure of scales in cones with a moisture content of 5% and 20%, as well as evaluated changes in cell wall thickness. The obtained results were compared with the structural investigations of scales conducted using scanning electron microscopy (SEM) of characteristic sites on the inner and outer sides of the scales. The greatest increment in the scale opening angle was noted on the first day of the process (34°) and in scales from the middle cone segment (39°). In scales with a moisture content of 5% and 20%, the greatest changes in cell wall thickness were recorded for large cells (57%). The inner and outer structure of scales differed in terms of the presence and size of cells depending on the moisture content of the cones (5%, 10%, or 20%). The study demonstrated that the moisture content of cones was the crucial determinant of the cellular structure and opening of scales in larch cones. The scale opening angle increased with decreasing moisture content but did not differ significantly for various segments of cones or various hours of the consecutive days of the process. This finding may lead to reducing the seed extraction time for larch cones. The internal and external structure of scales differed depending on moisture content, which also determined the size and wall thickness of cells.
... The specific mechanisms of a pinecone opening and closing is related to survival strategy, which allows the pine to disperse seeds over longer distances [10]. Consequently, the shape of the pinecone changes because the pinecone relates to water (moisture) in its external environment [11,12]. Since the pinecone is composed of dead cells, the operation of implementing the hygroscopic mechanism of the pineal scales can be disseminated into a passive mechanism [13]. ...
In order to better understand the functions of plants, it is important to analyze the internal structure of plants with a complex structure, as well as to efficiently monitor the morphology of plants altered by their external environment. This anatomical study investigated structural characteristics of pinecones to provide detailed descriptions of morphological specifications of complex cone scales. We analyzed cross-sectional image data and internal movement patterns in the opening and closing motions of pinecones, which change according to the moisture content of its external environment. It is possible to propose a scientific system for the deformation of complex pinecone for the variable structures due to changes in relative humidity, as well as the application of technology. This study provided a functional principle for a multidisciplinary approach by exploring the morphological properties and anatomical structures of pinecones. Therefore, the results suggest a potential application for use in energy-efficient materials by incorporating hygroscopic principles into engineering technology and also providing basic data for biomimicry research.
... Through the long-term process of evolution, the distributions of leaf veins have naturally developed into well-organized structures [5]. The common hypotheses regarding the morphic formation of these structures generally include auxin canalization [6], mechanical forces [7] and hydraulic architecture [8], according to which the vein distribution in a leaf is governed by criteria concerning potential energy minimization and balance [9]. Because of their excellent functionality in providing fluid transport and mechanical support, leaf vein networks have a wide range of potential bionic applications in engineering. ...
The stiffness and heat dissipation of thin planar structures in industrial engineering are taken as the background for this research. Plant leaves with various vein patterns, such as tobacco (Nicotiana tabacum L.) and chili (Capsicum annuum L.) leaves, are treated as the research objects. Through a combination of morphological and mechanical analysis, the distribution patterns and properties of leaf veins are mathematically characterized. A topological optimization algorithm is employed to simulate the vein growth process, thus revealing the effects of the mechanical and biological properties of different leaves on their vein morphologies. Additionally, the angles between the main and secondary veins are controlled to satisfy biological constraints. This comprehensive exploration of vein morphological formation can serve as a reference for the design of bionic thin planar structures in engineering.
... The use of isotropic, non-sensitive polymers creates greater differential hygroscopic swelling between the layers and, as a result, better control of actuation direction, precise angles, and response speed can J o u r n a l P r e -p r o o f 37 be achieved. However, the use of anisotropic properties in both active and passive layers could lead to an interesting bidirectional actuation as observed in biological systems such as the pine cone scale [192] [193]. ...
To date, the literature has focused on synthetic fibre-reinforced composites, but it has not adequately addressed the unique properties that differentiate natural from synthetic fibres, such as their natural variation in microstructure and composition across species. This review paper proposes a critical overview of the current state of 3D printing of natural fibre-reinforced composites or biocomposites for mechanical purposes, as well as an overview of their role in 4D printing for stimuli-responsive applications. The paper is structured as follows: after the first part recalling the specificities of natural fibres and their associated composites, the two main sections are each divided into two parts presenting an analysis of the available data to provide fundamental understandings and a discussion and outlook for the future.
Natural discontinuous fibre-reinforced polymers exhibit moderate mechanical properties compared to composites manufactured by conventional processes due to specific factors of the 3D printing process, such as high porosity, low fibre content, and a very low fibre-aspect ratio (L/d). Hygromorph BioComposites (HBC) are categorized into a new class of smart materials that could be used for 4D printing of shape-changing mechanisms. Fibre content, fibre orientation control, and fibre continuity are outlined in relation to known challenges in actuation performance.
... lambertiana), and it remains to be investigated which other species possess similar kinematics and how and why they have evolved. In a recent study [45], the interrelation of longitudinal and transverse curvature changes in P. pinaster cone scales, the environmental humidity regime and the scale shape and thickness has been quantitatively described, which further helps our understanding of complex shape changes in such natural actuators. ...
We developed biomimetic hygro-responsive composite polymer scales inspired by the reversible shape-changes of Bhutan pine ( Pinus wallichiana ) cone seed scales. The synthetic kinematic response is made possible through novel four-dimensional (4D) printing techniques with anisotropic material use, namely copolymers with embedded cellulose fibrils and ABS polymer. Multi-phase motion like the subsequent transversal and longitudinal bending deformation during desiccation of a natural pinecone scale can be structurally programmed into such printed hygromorphs. Both the natural concept generator (Bhutan pinecone scale) and the biomimetic technical structure (4D printed scale) were comparatively investigated as to their displacement and strain over time via three-dimensional digital image correlation methods. Our bioinspired prototypes can be the basis for tailored autonomous and self-sufficient flap and scale structures performing complex consecutive motions for technical applications, e.g. in architecture and soft robotics.
This article is part of the theme issue ‘Bioinspired materials and surfaces for green science and technology (part 3)’.
... Because of its low cost and short cycles, FFF has been widely applied in mechanical design [2], biomedical engineering [3,4], prototype fabrication [5] and topology optimization [6], among other fields. Due to its widespread use, this technology has a significant impact that will only increase in the future [7]. ...
Tool-path planning has a considerable impact on the quality of components printed by fused filament fabrication (FFF). This research proposes a path generation strategy based on the orientations of the maximum principal stresses. According to stress calculations from finite element analysis (FEA) of the components, tool-paths, which are programmed as parallel to the maximum principal stress directions, are constructed with the depth-first search (DFS) method and a connection criterion. The breakpoints in the tool-paths are then eliminated by connecting adjacent tool-paths. The Dijkstra algorithm is engaged to reduce the nozzle jump distance and shorten the production time. Stretching tests of different specimens printed with the developed path generation algorithms demonstrate that the model with the stress-based path has better mechanical performance. The digital image correlation (DIC) method and scanning electron microscopy (SEM) are employed to observe the fracture processes and fracture surfaces, respectively. Corresponding results of DIC and SEM reveal that different path filling forms exhibit variable failure patterns because of filament anisotropy. The filling fraction is calculated and indicates that the deposition quality of the advanced path is not compromised. This work provides a synthesis methodology for improving the mechanical performance of 3D printing products.
... In this paper, we apply the recently proposed discontinuity layout optimization (DLO) numerical approach [54][55][56][57] to quantitatively evaluate the stability of pre-grouted tunnel sections. DLO, which belongs to the family of topology optimization methods [58][59][60], introduces over one thousand nodes into the domain and connects every pair of nodes as a potential discontinuity for optimization. The target function is defined based on the minimization of energy, and the final solution is obtained automatically [61][62][63][64]; accordingly, this approach exhibits numerical stability and a high efficiency [65][66][67][68]. ...
Pre-grouting is a popular ground treatment strategy utilized to enhance the strength and stability of strata during the excavation of a tunnel through a fault zone. Two important questions need to be answered during such an excavation. First, how should the grouting size be determined? Second, when should excavation begin after grouting? These two questions are conventionally addressed through empirical experience and standard criteria because a reliable quantitative approach, which would be preferable, has not yet been developed. To address these questions, we apply a recently proposed numerical approach known as discontinuity layout optimization, an efficient node-based upper bound limit analysis method. A case study is provided utilizing a tunnel located in a stratum characterized by complicated geological conditions, including soft soil and a fault zone. The factor of safety is used to quantitatively assess the stability of the tunnel section. The influences of the grouted zone thickness and the time-dependent material properties of the grouted zone on the stability of the tunnel section are evaluated, thereby assisting designers by quantitatively assessing the effects of pre-grouting.
... Fused deposition modeling (FDM), a fast and direct additive manufacturing technology, prints structures by accumulating ejected warmed thermoplastic fibers layerby-layer [1] and has been widely adopted in prototype fabrication [2], biomedical engineering [3,4], bionic structures [5], electronic devices [6], and drug delivery [7]. This rapid manufacturing technique is becoming a popular area of research that has been advanced by innovative technologies, methods, and materials. ...
Additive manufacturing has the potential to provide novel solutions for fabricating complex structures. However, one of the main obstacles for such methods is the anisotropic mechanical properties of the manufactured product, which hinder the popularization of additive manufacturing in modern industries. Here, a simple yet versatile algorithm is introduced to produce isotropic products via optimizing the printing path. In this method, the workpiece is first separated into distinct areas in terms of the printing sequence, which increases the efficiency of the fabrication process. Subsequently, the printing path is schemed in each sub-region to allow a short extrusion length and low number of start-stop processes. Finally, this maze-like printing path is revised through a series of tensile tests and fracture surface analyses to validate the isotropy. Bending and indentation tests demonstrate that the samples present distinguished properties in terms of strength and isotropy in mechanical properties. Moreover, numerical and physical tests are implemented for validating the advantage of this maze-like pattern in preventing warping caused by residual stress. This work may play a significant role in printing molds that require isotropic properties.
... [1][2][3][4][5][6] To design intelligent morphing materials, nature has provided elegant paradigms and inspiring sources. [7][8][9] There are efforts devoted to understanding and mimicking the versatile deformations of natural systems, such as the bending of pinecones and wheat awns, [10][11][12] the snapping of the Venus flytrap, [13,14] and the twisting of Bauhinia variegate bean pod valves, [15] to name a few. Among the synthetic materials undergoing preprogrammed deformations, hydrogels are particularly interesting because of their open network structures and the drastic volume changes under the actions of external stimuli. ...
Self‐shaping materials have wide applications in soft robotics, biomedical devices, etc. Shape transformations of intelligent materials are usually realized by switching the environmental conditions. However, it is challenging to form multi‐stable morphing structures under the same condition. Here we demonstrate the programmed deformations of a composite hydrogel into multi‐stable configurations at the same condition. The hydrogel consists of integrated units of through‐thickness and/or in‐plane gradient structures, where the former leads to bending, folding, or twisting with pre‐determined direction and the latter buckles upward or downward with equal possibility. The bi‐stability of buckling affords the integrated hydrogel with multiple possible configurations. The composite hydrogel with multiple in‐plane gradient units (number: n) and through‐thickness gradient ones (number: m) theoretically has 2n×1m = 2n configurations under the same condition. Although the integration of units with through‐thickness gradient does not contribute to the diversity of configurations, it favors forming complex and designable configurations. Both experimental and simulation results show that various stable configurations can be obtained in one composite hydrogel under the same condition by controlling the buckling direction of each unit by a selective pre‐swelling step. This concept and strategy should be applicable for other intelligent materials and merit their applications in diverse areas. This article is protected by copyright. All rights reserved.
... About the iteration procedures, the interested reader is also referred to refs. [121][122][123][124][125][126][127][128][129][130]. ...
The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implicit representations of the cracks' topology are needed. CEM does not need remeshing technique, cover algorithm, nodal enrichment or specific crack tracking strategies. The crack opening is condensed in local element, greatly reducing the coding efforts and simplifying the numerical procedure. This paper presents numerical simulations with CEM regarding several benchmark tests, the results of which further indicate the capability of CEM in capturing complex crack growths referring propagations of existed cracks as well as initiations of new cracks.
... In this paper, we apply the recently proposed discontinuity layout optimization (DLO) numerical approach [54][55][56][57] to quantitatively evaluate the stability of pre-grouted tunnel sections. DLO, which belongs to the family of topology optimization methods [58][59][60], introduces over one thousand nodes into the domain and connects every pair of nodes as a potential discontinuity for optimization. The target function is defined based on the minimization of energy, and the final solution is obtained automatically [61][62][63][64]; accordingly, this approach exhibits numerical stability and a high efficiency [65][66][67][68]. ...
Pre-grouting is a popular ground treatment strategy utilized to enhance the strength and stability of strata during the excavation of a tunnel through a fault zone. Two important questions need to be answered during such an excavation. First, how should the grouting size be determined? Second, when should excavation begin after grouting? These two questions are conventionally addressed through empirical experience and standard criteria because a reliable quantitative approach, which would be preferable, has not yet been developed. To address these questions, we apply a recently proposed numerical approach known as discontinuity layout optimization , an efficient node-based upper bound limit analysis method. A case study is provided utilizing a tunnel located in a stratum characterized by complicated geological conditions, including soft soil and a fault zone. The factor of safety is used to quantitatively assess the stability of the tunnel section. The influences of the grouted zone thickness and the time-dependent material properties of the grouted zone on the stability of the tunnel section are evaluated, thereby assisting designers by quantitatively assessing the effects of pre-grouting.
Discontinuity layout optimization (DLO) is a relatively new upper bound limit analysis method. Compared to classic topology optimization methods, aimed at obtaining the optimum design of a structure by considering its self‐weight, building cost, or bearing capacity, DLO optimizes the failure pattern of the structure under specific loading conditions and constraints by minimizing the dissipation energy. In this work, we present a modified DLO algorithm that contains all of the advantages of DLO. It is referred to virtual displacement‐based discontinuity layout optimization (VDLO). VDLO takes the stress state of a loaded structure as a snapshot and correspondingly provides the optimum failure pattern, which greatly extends the application potential of DLO. Numerical examples indicate the effectiveness and flexibility of VDLO. It is regarded as a highly promising supplemental tool for other numerical methods in element‐/node‐based frameworks.
Changing consumer attitudes and food decisions drive the food industry to explore novel food technologies. Though 3D printing is a breakthrough technology, the advancements in additive manufacturing made a quantum leap in the development of novel four‐dimensional (4D) printing. Technically, 4D printing is an iteration of 2D and 3D printing with the additional physical transformation of material with time. 4D printing is becoming quite common in the nonfood sector (shape memory metals, alloys, ceramics, polymers, composites, and hydrogels). However, the principle of programming strategies of smart materials is yet to be studied in depth for food applications. Currently, 4D transformations (shape, volume, and color) are induced in 3D food constructs through internal (pH, moisture, and concentration difference) and external (temperature, pressure, and light) stimuli. The present chapter aims at explaining the concepts and basic principles of 4D printing. The major aspects and considerations such as printing method, nature and type of stimulus, the response of smart materials, and its interaction mechanism are highlighted. The selection of desired stimuli‐responsive programming materials is quite important, which must be compatible with the 3D printer for a successful 4D‐printing process. Various kinds of smart materials, working mechanisms of shape memory polymers, types of shape memory effect, stimuli‐responsive systems, and different programming strategies employed in 4D printing are detailed. In context with food, the programming strategies are limited with pH, moisture, temperature, and anisotropy. This chapter provides insights into the applicability of 4D printing in structural design and targeted transformations of novel 4D‐printed foods. Technical aspects such as the correlation of food structures and activation stimulus, innovative material properties, 3D printing and programming strategies, optimization of postprocessing, method evaluation, and validation are yet to be addressed in future research. Addressing these aspects would bridge up the research gap that exists in 4D food printing and brings out various feasibilities for the development of novel healthy smart foods.
In contrast to conventional hard actuators, soft actuators offer many vivid advantages, such as improved flexibility, adaptability, and reconfigurability, which are intrinsic to living systems. These properties make them particularly promising for different applications, including soft electronics, surgery, drug delivery, artificial organs, or prosthesis. The additional degree of freedom for soft actuatoric devices can be provided through the use of intelligent materials, which are able to change their structure, macroscopic properties, and shape under the influence of external signals. The use of such intelligent materials allows a substantial reduction of a device's size, which enables a number of applications that cannot be realized by externally powered systems. This review aims to provide an overview of the properties of intelligent synthetic and living/natural materials used for the fabrication of soft robotic devices. We discuss basic physical/chemical properties of the main kinds of materials (elastomers, gels, shape memory polymers and gels, liquid crystalline elastomers, semicrystalline ferroelectric polymers, gels and hydrogels, other swelling polymers, materials with volume change during melting/crystallization, materials with tunable mechanical properties, and living and naturally derived materials), how they are related to actuation and soft robotic application, and effects of micro/macro structures on shape transformation, fabrication methods, and we highlight selected applications.
Strength, toughness, and anisotropy are all important mechanical features in 3D printing. Unfortunately, strength and toughness are frequently antagonistic, making it difficult to improve both at the same time. Here, a biomimetic composite is proposed to increase both the strength and toughness with in-plane isotropy. The optimal rotational angle, ultimate strength and toughness can be improved around 100%, respectively, along with good in-plane isotropy. The mechanics of the improvement, the fracture surface is investigated, and a finite element (FE) simulation is carried out. By keeping the stress at a modest level and maximising the fracture surface during its propagation, ideal mechanical characteristics can be achieved at a specific rotational angle. This approach is straightforward, adaptable, and has the potential to provide good mechanical reinforcement in extrusion-based 3D printing. This paper provides a critical view of the state of the 3D printing of composites of natural fibre or biocomposites for mechanical purposes and an overview of their use in 4D printing in stimulating applications. Due to unique process advantages such as rising porosity, Natural discontinuous, improved polymers with a low fibre content and very low fibre aspect ratio (L/d) have mild mechanical properties in comparison with standard composites. Fibre material, fibre control and fibre quality are defined in response to established diagnostic problems.
Self‐assembly of three‐dimensional (3D) structures, through bending, twisting, folding, and buckling, has garnered broad interest among physicists, mathematicians, chemists, and biologists. Herein strain engineering and geometric frustration as an on‐demand strategy for fabricating spontaneous rolling “origami” structures with programmable multistability across multiple length scales are exploited. Through experiments, theory, and finite element simulations, it is demonstrated that a strain‐engineered bilayer structure can make a transition from a monostable, doubly curved shape to a neutrally stable, developable configuration, depending on a dimensionless parameter that is determined through the plate's geometry and misfit strain. In addition, the doubly curved region near the edge can play a significant role in deciding the final bending direction of the strained bilayer due to edge effects. A strain‐engineering approach is further proposed to generate various 3D structures by programming the geometry, misfit strain, and mechanical properties of the bilayer units, for instance, a self‐folding buckyball structure. These design principles have promising broad applications in constructing self‐deploying, stimuli‐responsible, and multifunctional devices across multiple length scales. Strain engineering and geometric frustration are exploited as an on‐demand strategy for fabricating spontaneous rolling “origami” structures with programmable multistability across multiple length scales. A strain‐engineered bilayer can transition from a monostable state to a neutrally stable helical configuration. The design principle has broad applications in self‐deployable, stimuli‐responsive, and multifunctional devices.
An improved protocol is proposed for preparation of a humidity-sensitive soft actuator through the layer-by-layer assembling of weight-ratio-variable composites of sodium alginate (SA) and polyvinyl alcohol (PVA) into laminated structures. The design induces non-uniform hygroscopicity in thickness direction and gives rise to strong interfacial interaction between layers, making the actuator with directional motility. A mathematic model reveals that the directional motion is driven by chemical potential of humidity, and its energy conversion efficiency from humidity to mechanical work reaches 81.2% at 25 °C. By coating with CoCl2, the composite film of [email protected]/CoCl2 can act as a warning sign that provides a reminding information to prevent people from slipping or falling by conspicuous red sign during the high-humidity environment. When the film is involved in a bidirectional switch, it is capable of turning on/off light emitting diodes by humidity, showing a promising potential in control over humidity-dependent devices.
Shape-shifting of flat materials into the desired 3D configuration is an alternative design route for fabrication of complex 3D shapes, which provides many benefits such as access to the flat material surface and the ability to produce well-described motions. The advanced production techniques that primarily work in 2D could then be used to add complex surface features to the flat material. The combination of complex 3D shapes and surface-related functionalities has a wide range of applications in biotechnology, actuators/sensors, and engineering of complex metamaterials. Here, we categorize the different programming strategies that could be used for planning the shape-shifting of soft matter based on the type of stresses generated inside the flat material and present an overview of the ways those mechanisms could be used to achieve the desired 3D shapes. Stress gradients through the thickness of the material, which generate out-of-plane bending moments, and compressive in-plane stresses that result in out-of-plane buckling constitute the major mechanisms through which shape-shifting of the flat matter could be programmed. We review both programming strategies with a focus on the underlying physical principles, which are highly scalable and could be applied to other structures and materials. The techniques used for programming the time sequence of shape-shifting are discussed as well. Such types of so-called “sequential” shape-shifting enable achieving more complex 3D shapes, as the kinematics of the movements could be planned in time to avoid collisions. Ultimately, we discuss what 3D shapes could be achieved through shape-shifting from flat soft matter and identify multiple areas of application.
Materials with switchable mechanical properties are widespread in living organisms and endow many species with traits that are essential for their survival. Many of the mechanically morphing materials systems found in nature are based on hierarchical structures, which are the basis for mechanical robustness and often also the key to responsive behavior. Many “operating principles” involve cascades of events that translate cues from the environment into changes of the overall structure and/or the connectivity of the constituting building blocks at various levels. These concepts permit dramatic property variations without significant compositional changes. Inspired by the function and the growing understanding of the operating principles at play in biological materials with the capability to change their mechanical properties, significant efforts have been made toward mimicking such architectures and functions in artificial materials. Research in this domain has rapidly grown in the last two decades and afforded many examples of bioinspired materials that are able to reversibly alter their stiffness, shape, porosity, density, or hardness upon remote stimulation. This review summarizes the state of research in this field.
Pine cones fold their scales when it rains to prevent seeds from short-distance dispersal. Given that the scales of pine cones consist of nothing but dead cells, this folding motion is evidently related to structural changes. In this study, the structural characteristics of pine cones are studied on micro-/macro-scale using various imaging instruments. Raindrops fall along the outer scales to the three layers (bract scales, fibers and innermost lignified structure) of inner pine cones. However, not all the layers but only the bract scales get wet and then, most raindrops move to the inner scales. These systems reduce the amount of water used and minimize the time spent on structural changes. The result shows that the pine cones have structural advantages that could influence the efficient motion of pine cones. This study provides new insights to understand the motion of pine cones and would be used to design a novel water transport system.
Nature displays numerous examples of materials that can autonomously change their shape in response to external stimuli. Remarkably, shape changes in biological systems can be programmed within the material's microstructure to enable self-shaping capabilities even in the absence of cellular control. Here, we revisit recent attempts to replicate in synthetic materials the shape-changing behavior of selected natural materials displaying deliberately tuned fibrous architectures. Simple processing methods like drawing, spinning or casting under magnetic fields are shown to be effective in mimicking the orientation and spatial distribution of reinforcing fibers of natural materials, thus enabling unique shape-changing features in synthetic systems. The bioinspired design and creation of self-shaping microstructures represent a new pathway to program shape changes in synthetic materials. In contrast to shape-memory polymers and metallic alloys, the self-shaping capabilities in these bioinspired materials originate at the microstructural level rather than the molecular scale. This enables the creation of programmable shape changes using building blocks that would otherwise not display the intrinsic molecular/atomic phase transitions required in conventional shape-memory materials.
Combination of soft active hydrogels with hard passive polymers gives rise to all-polymer composites. The hydrogel is sensitive to external stimuli while the passive polymer is inert. Utilizing the different behaviors of two materials subject to environmental variation, for example temperature, results in self-folding soft machines. We report our efforts to model the programmable deformation of self-folding structures with temperature-sensitive hydrogels. The self-folding structures are realized either by constructing a bilayer structure or by incorporating hydrogels as hinges. The methodology and the results may aid the design, control and fabrication of 3D complex structures from 2D simple configurations through self-assembly.
Chirality plays a significant role in the physical properties and biological functions of many biological materials, e.g., climbing tendrils and twisted leaves, which exhibit chiral growth. However, the mechanisms underlying the chiral growth of biological materials remain unclear. In this paper, we investigate how the Towel Gourd tendrils achieve their chiral growth. Our experiments reveal that the tendrils have a hierarchy of chirality, which transfers from the lower levels to the higher. The change in the helical angle of cellulose fibrils at the subcellular level induces an intrinsic torsion of tendrils, leading to the formation of the helical morphology of tendril filaments. A chirality transfer model is presented to elucidate the chiral growth of tendrils. This present study may help understand various chiral phenomena observed in biological materials. It also suggests that chirality transfer can be utilized in the development of hierarchically chiral materials having unique properties.
Fibonacci spirals are ubiquitous in nature, but the spontaneous assembly of such patterns has rarely been realized in laboratory. By manipulating the stress on Ag core/SiO2 shell microstructures, the authors obtained a series of Fibonacci spirals (3×5 to 13×21) of definite chirality as a least elastic energy configuration. The Fibonacci spirals occur uniquely on conical supports-spherical receptacles result in triangular tessellations, and slanted receptacles introduce irregularities. These results demonstrate an effective path for the mass fabrication of patterned structures on curved surfaces; they may also provide a complementary mechanism for the formation of phyllotactic patterns.
The scales of seed-bearing pine cones move in response to changes in relative humidity. The scales gape open when it is dry, releasing the cone's seeds1. When it is damp, the scales close up. The cells in a mature cone are dead, so the mechanism is passive: the structure of the scale and the walls of the cells composing the scale respond to changing relative humidity. Dissection of cones from the Monterey pine, Pinus radiata, revealed to us two types of scale growing from the main body of the cone — the ovuliferous scale and the bract scale. The larger ovuliferous scales respond to changes in relative humidity when removed from the body of the cone.
Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology.
The rapid closure of the Venus flytrap (Dionaea muscipula) leaf in about 100 ms is one of the fastest movements in the plant kingdom. This led Darwin to describe the plant as "one of the most wonderful in the world". The trap closure is initiated by the mechanical stimulation of trigger hairs. Previous studies have focused on the biochemical response of the trigger hairs to stimuli and quantified the propagation of action potentials in the leaves. Here we complement these studies by considering the post-stimulation mechanical aspects of Venus flytrap closure. Using high-speed video imaging, non-invasive microscopy techniques and a simple theoretical model, we show that the fast closure of the trap results from a snap-buckling instability, the onset of which is controlled actively by the plant. Our study identifies an ingenious solution to scaling up movements in non-muscular engines and provides a general framework for understanding nastic motion in plants.
The interaction between elasticity and capillarity is used to produce three
dimensional structures, through the wrapping of a liquid droplet by a planar
sheet. The final encapsulated 3D shape is controlled by tayloring the initial
geometry of the flat membrane. A 2D model shows the evolution of open sheets to
closed structures and predicts a critical length scale below which
encapsulation cannot occur, which is verified experimentally. This {\it
elastocapillary length} is found to depend on the thickness as , a
scaling favorable to miniaturization which suggests a new way of mass
production of 3D micro- or nano-scale objects.
Scanning and transmission electron microscopy reveal that SiOx/Si layers can
roll-up into microtubes and radial superlattices on a Si substrate. These
hybrid objects are thermally stable up to 850 C and emit light in the visible
spectral range at room temperature. For tubes disengaged from the substrate
surface, optically resonant emission with mode spacings inversely proportional
to the tube diameter are observed and agree excellently with those obtained
from Finite-Different-Time-Domain simulations. The resonant modes we record are
strictly polarized along the tube axis.
Buckling of soft matter is ubiquitous in nature and has attracted increasing interest recently. This paper studies the retractile behaviors of a spherical shell perforated by sophisticated apertures, attributed to the buckling-induced large deformation. The buckling patterns observed in experiments were reproduced in computational modeling by imposing velocity-controlled loads and eigenmode-affine geometric imperfection. It was found that the buckling behaviors were topologically sensitive with respect to the shape of dimple (aperture). The shell with rounded-square apertures had the maximal volume retraction ratio as well as the lowest energy consumption. An effective experimental procedure was established and the simulation results were validated in this study. Reconfigurable and reversible devices can rapidly respond to mechanical, thermal, chemical, electromagnetic and optical stimuli by changing their shapes and functionalities. Such active structures capable of smartly adapting to ambient environment widely exist in nature. For instance, some viruses can expand and retract their shell-like bodies by opening and closing the external apertures when the environmental pH changes 1,2
Self-folding of thin films is a more deterministic form of self-assembly wherein structures curve or fold up either spontaneously on release from the substrate or in response to specific stimuli. From an intellectual standpoint, the study of the self-folding of thin films at small size scales is motivated by the observation that a large number of naturally occurring materials such as leaves and tissues show curved, wrinkled, or folded micro- and nanoscale geometries. From a technological standpoint, such a self-assembly methodology is important since it can be used to transform the precision of existing planar patterning methods, such as electron-beam lithography, to the third dimension. Also, the self-folding of graphene promises a means to create a variety of three-dimensional carbon-based micro- and nanostructures. Finally, stimuli responsive self-folding can be used to realize chemomechanical and tether-free actuation at small size scales. Here, we review theoretical and experimental aspects of the self-folding of metallic, semiconducting, and polymeric films.
Utilisation of spontaneous deformation of polymer films for fabrication of self-assembling constructs is a novel and very attractive research field. This manuscript overviews recent advance in the development and application of wrinkling, creasing and folding polymer films in biotechnology.
Written by one of the world's leading authorities on plate behavior, this study gives a clear physical insight into elastic plate behavior. Small-deflection theory is treated in Part 1 in chapters dealing with basic equations: including thermal effects and multi-layered anisotropic plates, rectangular plates, circular and other shaped plates, plates whose boundaries are amenable to conformal transformation, plates with variable thickness, and approximate methods. Large-deflection theory is treated in Part 2 in chapters dealing with basic equations and exact solutions; approximate methods, including post-buckling behavior; and asymptotic theories for very thin plates, including tension field theory and inextensional theory. The mathematical content is necessarily high, making the style of the book appropriate to engineers and applied mathematicians. E.H. Mansfield is a Fellow of the Royal Society, a founder member of the Fellowship of Engineering, and the author of over 100 publications.
The bilocular seed capsules of species on the Acanthaceae subfamily Acanthoideae are either hygrochastic or xerochastic, but in both cases the mechanism for seed expulsion is similar; only the “trigger” differs in the two instances. The drying of the capsule results in the storage of elastic energy in the capsule valves. The failure of the seam joining the two values precipitates the conversion of the elastic potential energy stored in the valves and seeds. In the hygrochastic case the failure is due to moisture absorption on wetting of the capsule beak which weakens the pectic “glue”; in the xerochastic case the seam failure is due simply to the high stress in the bonding layer at some degree of desiccation. This paper explains quantitatively how the anatomy of the capsule efficiently imports high initial expulsion velocity to the seeds in order to maximize their range. The specific example considered inRuellia brittonianaLeonard, a cultivated shrub native to Mexico, but the situation is similar for the entire Acanthoideae subfamily.
Natural frequencies of rectangular plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generated by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. Natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods. The method yields superior results for lower modes, particularly when plates have some of the edges free.
The post-fire regenerative ability of Pinus halepensis, Pinus nigra and Pinus sylvestris, three of the most important pine species present in the West Mediterranean basin, has been analyzed in the light of seed tolerance to different temperatures and times of exposure, and of seed position during the fire event (seeds inside cones versus free seeds). The combination of different fire intensities and degrees of seed protection allows us to draw different scenarios during the fire event: canopy scenarios (seeds inside cones), surface scenarios (seeds on the ground surface), and soil scenarios (seeds in the top soil layers). There were interspecific differences in the pattern of cone opening under the different heat treatments: cones of P.nigra and P.sylvestris showed similar percentages of opening, but considerably higher than those of P.halepensis. In the three species, seeds inside cones showed higher percentages of germination than those that were free, emphasizing the important role of cones in the protection of pine seeds from high temperatures. The percentage of germination decreased when both the temperature and the time of exposure increased, and there was also a significant species effect: P.halepensis showed higher germination rates than P.nigra, and both were higher than P.sylvestris. The overall scores of seed germination of these three pine species under the conditions tested suggests that their regeneration after fire should come either from the soil bank, or from the canopy bank, but rarely from the ground surface. As the existence of a permanent seed bank in Mediterranean pines is probably limited or nil, pine recruitment after fire appears to be mainly controlled by the existence of a canopy seed bank. The contribution of this canopy bank to the differences in postfire regeneration success of the three pine species is discussed in the light of their seeding phenology and the effects of fire severity on cone opening. The results obtained in this study contribute to explain the successful regeneration of P.halepensis, and the failure of P.nigra and P.sylvestris after fire.
In this paper, we detail a strategy to self-assemble microstructures using chromium/copper (Cr/Cu) bilayers. Self-assembly was primarily driven by the intrinsic residual stresses of Cr within these films; in addition, the degree of bending could be controlled by changing the Cu film thickness and by introducing a third layer with either a flexible polymer or a rigid metal. We correlate the observed curvature of patterned self-assembled microstructures with those predicted by a published multilayer model. In the model, measured stress values (measured on the unpatterned films using a substrate curvature method) were utilized. We also investigated the role of two different sacrificial layers: 1) silicon and 2) water-soluble polyvinyl alcohol. Finally, a Taguchi design of experiments was performed to investigate the importance of the different layers in contributing to the stress-thickness product (the critical parameter that controls the curvature of the self-assembled microstructures) of the multilayers. This paper facilitates a deeper understanding of multilayer thin-film-based self-assembly and provides a framework to assemble complex microstructures, including tetherless self-actuating devices.
Silicon nitride membranes were nanopatterned and then folded into three-dimensional (3D) configurations. The out-of-plane folding was achieved using stressed metal hinges. The concept of folding nanopatterned membranes into 3D shapes is referred to as nanostructured origami because of the similarity to the Japanese paper-art of origami, in which two-dimensional surfaces are folded into volumetric shapes. The stressed metal hinges were modeled analytically and compared to experiment. Experimental results demonstrated controllable folding of nanopatterned silicon nitride membranes.
The three-dimensional patterns of surface wrinkling on a core-shell soft sphere are investigated through buckling and postbuckling analyses under differential tissue growth or shrinkage. With increasing deformation, the sphere first exhibits a buckyball-like wrinkling pattern and then undergoes a wrinkle-to-fold transition into labyrinth folded patterns, in agreement with experimental observations. This transition involves dynamic movement, rotation, and coalescence of polygons formed during the initial buckling.
(Figure Presented) We demonstrate the concept of inducing stresses in thin films post-deposition (extrinsic stress) to curve nanostructures on demand. The remarkably high extrinsic stress, induced by triggering grain coalescence in Sn thin films, was used to selfassemble 3D nanostructures with radii of curvature as small as 20 nm. The fabrication methodology required only simple processing steps and the self-assembly process was highly parallel. Curved nanostructures with any desired pattern and both homogeneous (rings, tubes) and variable radii of curvature (spirals, talons) could be constructed.
Origami, the ancient Japanese art of paper folding, is mathematically deeper than it looks. Delving into its complexities allows the construction of elaborate and useful structures from simple, flat templates. Over the past two decades, mathematicians and engineers have been exploring and developing the science of folding objects flat. In the process they have looked at how origami, both as it occurs in the natural world in unfolding leaves and insects' wings and as the ancient Japanese art, can inform their knowledge.
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